The 22-year-old clocked 13.05 seconds to finish 12 hundredths of a second ahead of Spain's Orlando Ortega in the final at Rio's Olympic stadium on Tuesday. France's Dimitri Bascou took bronze in 13.24, Xinhua news agency reported.
He said the success of Bolt and Fraser-Pryce, who have won nine Olympic gold medals between them, has rubbed off on other Jamaican athletes.
"You just feed off them; Bolt, Fraser Pryce and all those athletes you look up to. It's contagious," McLeod said.
"The feeling is indescribable. I honestly don't know what is going through my mind right now. I need to go back and recite 'you are an Olympic champion'."
McLeod, who is Jamaica's first men's 110m hurdles champion, said he never lost belief despite falling in two Diamond League meeting races this year.
"It's been an up and down year. It was kind of a humbling experience. I came to the realisation that things happen in sport. You are never guaranteed a perfect career. It was a test of character and I bounced back well.
"I came in to this championship like it [the falls] never happened. I just needed to trust my ability and have fun. I learned a lot from it," McLeod said.
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